Cutting an Object with a Plane Using Boolean Modifier
Since Blender 2.91, you can boolean with manifold objects like a Plane.
There are two methods now. The Exact method should solve your issue.
old 2.9x Fast (2.8 method)

new 2.9x Exact

It is cut out in inside normal direction (red color when Face Orientation overlay enabled).


If you still need to work in 2.8 you would have to use Solidify modifier or other tech to create non-manifold object as you mentioned.